Residence time distribution averaging uniformity

Stirred-tank reactors differ from plug flow reactors in that not aU fluid elements remain in the CSTR for the same length of time. The characteristics of the residence-time distribution function are treated in Chapter 11. In this subsection we consider only the problem of determining the average residence time of a fluid element in an ideal CSTR. This problem is simplified considerably by the fact that the fluid properties are uniform throughout the reactor... 

Single pass residence times are 0.5-3 sec, but most commercial operations employ some recycling of the product so that average residence times are brought up to 60 sec. Recycling also serves to condition the feed if it is very wet. The spread of residence times in pneumatic dryers, as indicated by Figure 9.5(a), is broad, so feed that has a particularly wide size distribution may not dry uniformly. Recycling, however, assists uniformity, or several dryers in series or preclassification of particle sizes may be employed. 

The most important, factors affecting the design of a fluid-solid noncatalytic reactor are the flow patterns of solid and fluid in the vessel. As noted in Sec. 14-1, the simplest case is where the composition of the fluid phase is uniform. Then the conversiori-vs-time relationship for single particles, such as Eq. (14-19), can be employed, along with the residence-time and particle-size distributions of the solid phase, to evaluate the average conversion. This problem is considered in the next section. When the fluid phase does not have a uniform composition the design is more complex. However, quantitative treatment is possible when the flow patterns of both solid and fluid phases are well defined. These kinds of reactors are discussed in Sec. 14-6. 

The time t is the contact time or residence time of molecules in the reactor. In the batch reactor, it is assumed that measured time is equal to the average contact time. However, in a continuous system, this time may or may not be equal to the contact time, because the distribution of molecules or properties (in the reactor inside) may not be uniform (or homogeneous), and it depends on the type of flow. Therefore, it is impossible to determine the kinetic properties without knowing the true reaction time. 

In a backmixed reactor, the conversion of reactants is controlled by the average length of time fluid elements remain in the reactor (their residence time). The ratio of the volume of fluid in the tank to the volumetric flow rate of the exit stream determines the residence time. Recall that in an ideal system of this type, operating at steady state, concentrations in the vessel are uniform and equal to those in the exit stream and thus the reaction rate is maintained at a constant value. Conversion of individual reactants and yield of specific products can be determined simply by multiplying the appropriate rate of interest by the residence time. With imperfect mixing, fluid elements have a distribution of residence times and the performance of the reactor is clearly altered. 

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